Nonsmooth differential-algebraic equations in chemical engineering

This chapter advocates a nonsmooth differential-algebraic equations (DAEs) modeling paradigm for dynamic simulation and optimization of continuous pharmaceutical process operations. Process intensification of pharmaceuticals production by continuous manufacturing is challenged by short campaigns, due to the low volume of some products. This calls for optimization of the entire dynamic campaign to achieve the highest overall yields, productivity and minimize waste. A variety of processes prevailing in the pharmaceutical industry are traditionally viewed as exhibiting hybrid continuous and discrete (i.e. discontinuous) behavior. In many cases such behavior is actually nonsmooth, rather than discontinuous. For such cases a distinction has not always been made, and these can be readily modeled by nonsmooth DAEs. A computationally relevant theory of nonsmooth DAEs (i.e. well-posedness and sensitivity analysis) has recently been established which is suitable for numerical implementations that scale efficiently for large-scale dynamic optimization problems.This chapter gives a brief overview of the nonsmooth DAEs framework. Such a formulation has been recently shown to admit a unique solution and computationally tractable sensitivity analysis, facilitating its embedding in optimization schemes to find optimal operational procedures. The mathematical modeling of selected processes using nonsmooth DAEs is outlined in detail. The nonsmooth dynamics of several units are illustrated. We then demonstrate how the overall campaign performance can be optimized in terms of on-specification productivity and yield, which are considered as objectives given a short time horizon for the production campaign. The optimal solutions give very valuable insights regarding the best start-up and shutdown procedures.

During the last three decades, the research area of systems engineering has emerged as a domain of fundamental importance and major impact within chemical engineering, as well as a cornerstone area in interdisciplinary research initiatives with computer science, operations research, applied mathematics, materials and life sciences. This is attributed to the unique characteristics of systems engineering which are the combination of analysis and synthesis for the design, optimization, and operation of processes and products. The product and process discovery research efforts are founded on fundamental advances in mathematical modeling, optimization theory and algorithms, and insights derived either from existing operations and/or from biology, chemistry, and physics. The fundamental advances are epitomized through new theoretical, algorithmic, and modeling frameworks for (a) mixed-integer linear and nonlinear optimization, (b) deterministic global optimization, and (c) dynamic simulation and optimization. The proposed modeling and optimization approaches have multiscale applications ranging from macroscopic to mesoscopic to microscopic systems, and which provide a natural and fundamental link between systems engineering, computational chemistry, computational biology and systems biology. Approaches based on mixed-integer linear and nonlinear optimization which were typically identified with process synthesis, scheduling and planning applications, have entered the domains of gene regulatory networks, metabolic networks, signal transduction networks, beta-sheet topology prediction in proteins, de novo peptide and protein design, DNA recombination, phase problem in X-ray crystallography, side chain optimization in protein prediction, peptide identification via tandem mass spectroscopy. Approaches based on deterministic global optimization associated with process design, synthesis, scheduling, and pooling/blending applications, are now in the main stream of product design, structure prediction in protein folding, dynamics of protein folding, NMR protein structure refinement, and de novo protein design. Approaches based on dynamic models and large scale optimization which were identified with process models and their applications, are suited for metabolic and signal transduction networks. As a result, a synergism between systems engineering, computational biology, and systems biology has evolved gradually, opened new research avenues and has reached the stage where fascinating research contributions address important questions in computational biology with methods and tools from systems engineering which combine mathematical rigor with key biological insights. This article provides a perspective on the challenges and opportunities that emerge from the fundamental developments in the research fields of systems engineering and computational biology. The advances in the areas of deterministic global optimization and process scheduling are introduced first, followed by their respective research opportunities. The revolution of genomics is discussed next with a particular focus on the advances and challenges in the areas of structure prediction in protein folding, de novo peptide and protein design, and peptide and protein identification via tandem mass spectroscopy. This article is based on material presented as an invited talk at the session on “The Future of Chemical Engineering Research III” during the 2004 annual AIChE meeting.

Optimization of process operations in the leather industry

Dynamic program optimizations are critical for the efficiency of applications in managed programming languages and scripting languages. Recent studies have shown that exploitation of program inputs may enhance the effectiveness of dynamic optimizations significantly. However, current solutions for enabling the exploitation require either programmers' annotations or intensive offline profiling, impairing the practical adoption of the techniques.This current work examines the basic feasibility of transparent integration of input-consciousness into dynamic program optimizations, particularly in managed execution environments. It uses transparent learning across production runs as the basic vehicle, and investigates the implications of cross-run learning on each main component of input-conscious dynamic optimizations. It proposes several techniques to address some key challenges for the transparent integration, including randomized inspection-instrumentation for cross-user data collection, a sparsity-tolerant algorithm for input characterization, and selective prediction for efficiency protection. These techniques make it possible to automatically recognize the relations between the inputs to a program and the appropriate ways to optimize it. The whole process happens transparently across production runs; no need for offline profiling or programmer intervention. Experiments on a number of Java programs demonstrate the effectiveness of the techniques in enabling input-consciousness for dynamic optimizations, revealing the feasibility and potential benefits of the new optimization paradigm in some basic settings.

BackgroundBrain, heart and skeletal muscle share similar properties of excitable tissue, featuring both discrete behavior (all-or-nothing response to electrical activation) and continuous behavior (recovery to rest follows a temporal path, determined by multiple competing ion flows). Classical mathematical models of excitable cells involve complex systems of nonlinear differential equations. Such models not only impair formal analysis but also impose high computational demands on simulations, especially in large-scale 2-D and 3-D cell networks. In this paper, we show that by choosing Hybrid Automata as the modeling formalism, it is possible to construct a more abstract model of excitable cells that preserves the properties of interest while reducing the computational effort, thereby admitting the possibility of formal analysis and efficient simulation.ResultsWe have developed CellExcite, a sophisticated simulation environment for excitable-cell networks. CellExcite allows the user to sketch a tissue of excitable cells, plan the stimuli to be applied during simulation, and customize the diffusion model. CellExcite adopts Hybrid Automata (HA) as the computational model in order to efficiently capture both discrete and continuous excitable-cell behavior.ConclusionsThe CellExcite simulation framework for multicellular HA arrays exhibits significantly improved computational efficiency in large-scale simulations, thus opening the possibility for formal analysis based on HA theory. A demo of CellExcite is available at .

This paper discusses the initial steps towards the formulation and implementation of a generic and flexible model centric framework for integrated simulation, estimation, optimization and feedback control of polymerization processes. For the first time it combines the powerful capabilities of the automatic continuous on-line monitoring of polymerization system (ACOMP), with a modern simulation, estimation and optimization software environment towards an integrated scheme for the optimal operation of polymeric processes. An initial validation of the framework was performed for modelling and optimization using literature data, illustrating the flexibility of the method to apply under different systems and conditions. Subsequently, off-line capabilities of the system were fully tested experimentally for model validations, parameter estimation and process optimization using ACOMP data. Experimental results are provided for free radical solution polymerization of methyl methacrylate.

Problem formulations and algorithms are considered for optimization problems with differential-algebraic equation (DAE) models. In particular, we provide an overview of direct methods, based on nonlinear programming (NLP), and indirect, or variational, methods. We further classify each method and tailor it to the appropriate applications. For direct methods, we briefly describe current approaches including the sequential approach (or single shooting), multiple shooting method, and the simultaneous collocation (or direct transcription) approach. In parallel to these strategies we discuss NLP algorithms for these methods and discuss optimality conditions and convergence properties. In particular, we present the simultaneous collocation approach, where both the state and control variable profiles are discretized. This approach allows a transparent handling of inequality constraints and unstable systems. Here, large scale nonlinear programming strategies are essential and a novel barrier method, called IPOPT, is described. This NLP algorithm incorporates a number of features for handling large-scale systems and improving global convergence. The overall approach is Newton-based with analytic second derivatives and this leads to fast convergence rates. Moreover, it allows us to consider the extension of these optimization formulations to deal with nonlinear model predictive control and real-time optimization. To illustrate these topics we consider a case study of a low density polyethylene (LDPE) reactor. This large-scale optimization problem allows us to apply off-line parameter estimation and on-line strategies that include state estimation, nonlinear model predictive control and dynamic real-time optimization.

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014

This paper aims to enhance feature detection in geophysical seismic data by advancing Arthur E. Barnes’s 2002 shaded relief method. Our primary objective is to integrate a 3D gradient operator into the existing workflow, thereby improving the clarity of geological structures and enhancing interpretability across the entire seismic volume. Building upon Barnes’s method, which utilizes dip-azimuth attributes and directional illumination, our approach introduces several methodological improvements. We compute amplitude-derived gradients at the voxel level using a 3D gradient operator and incorporate these gradient vectors into the shaded relief algorithm. This integration enhances the visibility of subtle structural and stratigraphic features by improving illumination cues. Furthermore, we dynamically optimize "degree" and "azimuth" parameters, allowing for more adaptive illumination based on the characteristics of each slice. Finally, we merge the original seismic amplitude information with the shaded relief output, resulting in a more comprehensive and geologically interpretable volumetric representation. Our enhanced technique demonstrates superior effectiveness in highlighting both structural and stratigraphic features compared to Barnes’s original method. By integrating the 3D gradient operator, we reveal subtle variations in fault planes and reflectors, leading to improved clarity and interpretability. Applications on field datasets illustrate how dynamic parameter optimization—combined with gradient-based shading and subsequent data fusion—sharpens fault delineation and emphasizes complex geological details that were previously indistinct. This outcome underscores the value of tailoring illumination parameters to localized features, leading to a deeper understanding of subsurface morphology. Overall, the proposed framework provides a streamlined and robust means for advanced seismic volume interpretation. The equipment used in this research includes a high-performance computer with advanced graphics capabilities, seismic data processing software, and a 3D visualization system. These tools were essential for implementing the 3D gradient operator and dynamic parameter optimization. The high-performance computer handled the complex computations involved in processing seismic data, while the seismic data processing software facilitated the integration of the enhanced algorithm into the workflow. The 3D visualization system allowed for detailed analysis and interpretation of the seismic volume. Testing involved applying the method to various seismic datasets to evaluate its effectiveness in different geological settings. An unusual aspect of our approach was the dynamic optimization of illumination parameters, which required iterative testing and refinement to achieve optimal results. The equipment proved highly effective in handling the complex computations involved, demonstrating its suitability for advanced seismic interpretation tasks. This study contributes a novel gradient-based enhancement to Barnes’s shaded relief method, with dynamically optimized illumination parameters and a data-fusion approach. These innovations offer superior delineation of subsurface features, boosting the existing body of knowledge for fault detection and geological interpretation in the petroleum industry. The integration of advanced equipment and methodologies underscores the potential for continued advancements in seismic data analysis, ultimately contributing to more accurate and efficient energy exploration.

Chapter 6 - Application of stochastic evolutionary optimization techniques to chemical processes

Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

Framework for a smart data analytics platform towards process monitoring and alarm management

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem and modeling of Hybrid Dynamical Systems (HDS). Generally speaking, HDS is a system mixing continuous and discrete behaviors that cannot be faithfully modeled neither by using formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We use the well known framework of hybrid automata for modeling hybrid systems, because they combine the continous and discretes parts on the same structure. Hybrid automaton is a states-transitions graph, whose dynamic evolution is represented by discretes and continous steps alternations, also, continous evolution happens in the automaton apexes, while discrete evolution is realized by transitions crossing (arcs) of the graph. Their simulation presents many problems mainly the synchronisation between the two models. Stateflow, used to describe the discrete model, is co-ordinated with Matlab, used to describe the continuous model. This article is a description of a case study, which is a two tanks system.

Model-based control of a simulated moving bed chromatographic process for the separation of fructose and glucose

Accurately predicting program behaviors (e.g., memory locality, method calling frequency) is fundamental for program optimizations and runtime adaptations. Despite decades of remarkable progress, prior studies have not systematically exploited the use of program inputs, a deciding factor of program behaviors, to help in program dynamic optimizations. Triggered by the strong and predictive correlations between program inputs and program behaviors that recent studies have uncovered, the dissertation work aims to bring program inputs into the focus of program behavior analysis and program dynamic optimization, cultivating a new paradigm named input-centric program behavior analysis and dynamic optimization.;The new optimization paradigm consists of three components, forming a three-layer pyramid. at the base is program input characterization, a component for resolving the complexity in program raw inputs and extracting important features. In the middle is input-behavior modeling, a component for recognizing and modeling the correlations between characterized input features and program behaviors. These two components constitute input-centric program behavior analysis, which (ideally) is able to predict the large-scope behaviors of a program's execution as soon as the execution starts. The top layer is input-centric adaptation, which capitalizes on the novel opportunities created by the first two components to facilitate proactive adaptation for program optimizations.;This dissertation aims to develop this paradigm in two stages. In the first stage, we concentrate on exploring the implications of program inputs for program behaviors and dynamic optimization. We construct the basic input-centric optimization framework based on of line training to realize the basic functionalities of the three major components of the paradigm. For the second stage, we focus on making the paradigm practical by addressing multi-facet issues in handling input complexities, transparent training data collection, predictive model evolvement across production runs. The techniques proposed in this stage together cultivate a lifelong continuous optimization scheme with cross-input adaptivity.;Fundamentally the new optimization paradigm provides a brand new solution for program dynamic optimization. The techniques proposed in the dissertation together resolve the adaptivity-proactivity dilemma that has been limiting the effectiveness of existing optimization techniques. its benefits are demonstrated through proactive dynamic optimizations in Jikes RVM and version selection using IBM XL C Compiler, yielding significant performance improvement on a set of Java and C/C++ programs. It may open new opportunities for a broad range of runtime optimizations and adaptations. The evaluation results on both Java and C/C++ applications demonstrate the new paradigm is promising in advancing the current state of program optimizations.